Effective Lagrangians for Scalar Fields and Finite Size Effects in Field Theory

TL;DR

This paper develops an effective field theory approach for scalar fields with multiple mass scales in bounded regions, analyzing boundary conditions and renormalization at one-loop level.

Contribution

It introduces a method to implement renormalization in lambda phi^4 theory with boundaries, considering different boundary conditions and multiple mass scales.

Findings

Renormalization scheme successfully applied to bounded scalar field theories.

Boundary conditions significantly affect the renormalization process.

One-loop corrections are computed for scalar fields with two mass scales.

Abstract

We discuss the approach of effective field theory on a d-dimensional Euclidean space in a scalar theory with two different mass scales in the presence of flat surfaces. Then considering Dirichlet and Neumann boundary conditions, we implement the renormalization program in the lambda phi^{4} theory in a region bounded by two parallel hyperplanes in the one-loop approximation.